Upper bounds for the moduli of polynomial-like maps

被引:0
|
作者
Blokh, Alexander [1 ]
Oversteegen, Lex [1 ]
Timorin, Vladlen [2 ]
机构
[1] Univ Alabama Birmingham, Dept Math, Birmingham, AL 35294 USA
[2] HSE Univ, Moscow 119048, Russia
关键词
complex dynamics; polynomial-like map; renormalization; Julia set; DYNAMICS; INEQUALITY;
D O I
10.1088/1361-6544/ad1aec
中图分类号
O29 [应用数学];
学科分类号
070104 ;
摘要
We establish a version of the Pommerenke-Levin-Yoccoz inequality for the modulus of a polynomial-like (PL) restriction of a polynomial and give two applications. First we show that if the modulus of a PL restriction of a polynomial is bounded from below then this restricts the combinatorics of the polynomial. The second application concerns parameter slices of cubic polynomials given by the non-repelling multiplier of a fixed point. Namely, the intersection of the so-called Main Cubioid and the multiplier slice lies in the closure of the principal hyperbolic domain, with possible exception of queer components.
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页数:24
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